ONE WAY ANOVA
The oneway analysis of variance (ANOVA) is used to determine whether there is any significant difference between the means of a dependent variable for three or more unrelated groups of an independent variable. Oneway ANOVA is particularly used when there is only one independent variable and one dependent variable. The dependent variable is metric (interval or ratio scale) whereas the independent variable is categorical or nominal in nature.
CASE ANALYSIS1
PROBLEM
A manager of XYZ electric bulbs Company wants to compare the life span of three different brands of bulbs available in the market. The manger collected the data of life span of the bulbs of brands A, B and C measured in hundreds of hours during three months period as shown below.
Table1: Sample Data
The purpose is test whether the lifetimes of four brands of electric bulbs are equal or not.
The hypotheses for the analysis are:
Null hypothesisH_{0}: The mean lifetimes for three brands of bulbs are equal.
Alternative Hypothesis H_{1}: The mean life time of at least two brands of bulbs differ.
Input Data
The variable ‘life time’ is dependent variable and the variable ‘brand’ is independent variable. The independent variable is coded as: 1 = Brand A, 2 = Brand B, 3 = Brand C. The following table depicts the dependent variable along with the coded independent variable and it is treated as the input data matrix for the analysis.
Table2: Input Data
Performing the Analysis with SPSS
For SPSS Version 11, click on Analyze ⇒ Compare Means ⇒ Oneway ANOVA
This will bring up the SPSS screen dialogue box as shown below.
After clicking OneWay ANOVA, this will bring up the following SPSS screen dialogue box
Select the dependent variable and move it to the Dependent list box. Similarly select the coded variable and move it to Factor box.
Now, click OK to get the output.
SPSS Output
The SPSS output of the analysis is given in the following table.
Table3: ANOVA
Lifetime
From the output, F = 1.473
DECISION
Reject the null hypothesis if pvalue (Sig. value) ≤ 0.05
INTERPRETATION
The pvalue is 0.302 and it is less than 0.05 (5% level of significance), so we reject the null hypothesis and accept the alternative hypothesis at 5% level of significance. It can be concluded that the life span of different brands of bulbs differ significantly.
CASE ANALYSIS2
PROBLEM
A pen manufacturing unit is interested to compare the average sales of its four salesmen X, Y, Z and W. The following depicts the weekly sales by the salesmen in hundreds of units.
Table1: Sample Data
The purpose is test whether the lifetimes of four brands of electric bulbs are equal or not.
The hypotheses for the analysis are:
Null hypothesisH_{0}: The average sales by three salesmen are equal.
Alternative Hypothesis H_{1}: The average sales of at least two salesmen differ.
Input Data
The variable ‘sales’ is dependent variable and the variable ‘salesmen’ is independent variable. The independent variable is coded as: 1 = Salesman X, 2 = Salesman Y, 3 = Salesman Z, 4 = Salesman W. The following table is used as the input data for the analysis.
Table2: Input Data
SPSS Output
The SPSS output of the analysis is given in the following table.
Table3: ANOVA
From the output, F = 0.392
DECISION
Reject the null hypothesis if pvalue (Sig. value) ≤ 0.05
INTERPRETATION
The pvalue is 0.762 and it is more than 0.05 (5% level of significance), so we accept the null hypothesis and conclude that the average sales by the salesmen do not differ significantly.
SPSS Command
 Click on ANALYZE at the SPSS menu bar (in older versions of SPSS, click on STATISTICS instead of ANALYZE).
 Click on COMPARE MEANS followed by ONE WAY ANOVA.
 Select the appropriate variable and move it to the DEPENDENT LIST. Similarly select the CODED variable and move it to FACTOR BOX.
 Click OK to get the output.
